arXiv:cond-mat/0506016 · Physical Review A

Landau damping of Bogoliubov excitations in two- and three-dimensional optical lattices at finite temperatures

Shunji Tsuchiya, Allan Griffin

Published Nov 18, 2005• 24 citations

Abstract

We study the Landau damping of Bogoliubov excitations in two- and three-dimensional optical lattices at finite temperatures, extending our recent work on one-dimensional (1D) optical lattices. We use a Bose-Hubbard tight-binding model and the Popov approximation to calculate the temperature dependence of the number of condensate atoms ${n}^{\mathrm{c}0}(T)$ in each lattice well. As with 1D optical lattices, damping only occurs if the Bogoliubov excitations exhibit anomalous dispersion (i.e., the excitation energy bends upward at low momentum), analogous to the case of phonons in superfluid $^{4}\mathrm{He}$. This leads to the disappearance of all damping processes in a $D$-dimensional simple cubic optical lattice when $U{n}^{\mathrm{c}0}\ensuremath{\geqslant}6DJ$, where $U$ is the on-site interaction, and $J$ is the hopping matrix element.

DOI: 10.1103/physreva.72.053621

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arXiv:cond-mat/0506016 · Physical Review A

Landau damping of Bogoliubov excitations in two- and three-dimensional optical lattices at finite temperatures

Shunji Tsuchiya, Allan Griffin

Published Nov 18, 2005• 24 citations

arXiv HTML PDF

Abstract

{n}^{\mathrm{c}0}(T)

in each lattice well. As with 1D optical lattices, damping only occurs if the Bogoliubov excitations exhibit anomalous dispersion (i.e., the excitation energy bends upward at low momentum), analogous to the case of phonons in superfluid

^{4}\mathrm{He}

. This leads to the disappearance of all damping processes in a

D

-dimensional simple cubic optical lattice when

U{n}^{\mathrm{c}0}\ensuremath{\geqslant}6DJ

, where

U

is the on-site interaction, and

J

is the hopping matrix element.

DOI: 10.1103/physreva.72.053621

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{n}^{\mathrm{c}0}(T)

^{4}\mathrm{He}

. This leads to the disappearance of all damping processes in a

D

-dimensional simple cubic optical lattice when

U{n}^{\mathrm{c}0}\ensuremath{\geqslant}6DJ

, where

U

is the on-site interaction, and

J

is the hopping matrix element.

^{4}\mathrm{He}

. This leads to the disappearance of all damping processes when $U{n}^{\mathrm{c}0}\ensuremath{\geqslant}6J$, where

U

is the on-site interaction,

J

is the hopping matrix element, and

{n}^{\mathrm{c}0}(T)

is the number of condensate atoms at a lattice site. This phenomenon also occurs in two-dimensional and three-dimensional optical lattices. The disappearance of Beliaev damping above a threshold wave vector is noted.